此算法改编自邓俊辉教授的《数据结构（C++语言版）》一书，原算法可参见原书或这篇博客：https://blog.csdn.net/wddpfx/article/details/82082724
鉴于原算法基于较多功能，我们平时使用AVL树时并不需要，特地改写一遍，希望各位指正。有BUG的话请留言。
以下算法下载链接 链接: https://pan.baidu.com/s/1dcpPvfEYB2L0iDdwnnMsRQ 密码: cx61

#include <iostream>
#include <vector>
#include <stack>
#include <queue>
#include <algorithm>

using namespace std;

struct Node
{
    int data;
    int height;
    int level;

    Node* father, *lchild, *rchild;
};


Node* creatAVLTree(vector<int> vec);
void insert(Node* &root, int);
void deleteX(Node* root, int);
Node* findNode(Node* root, int x);
Node* findPreNode(Node* root);
Node* findSucNode(Node* root);

//统一平衡算法
bool isBalance(Node* root);
Node* reBalance(Node* root);
int updateHeight(Node* root);
Node* findBadSubTree(Node*);//先序遍历寻找失衡子树
Node* getSubBadTree(Node*);//查找失衡子树的较高孩子节点
void connect34(Node* a, Node* b, Node* c, Node* T0, Node* T1, Node* T2, Node* T3);

//层次遍历输出元素
void levelTraversal(Node* root);

int main()
{
    //vector<int> vec = { 0, 8, 10, 34, 88, 2, 4, 6, 1, 990, 1000, 99, 20, 19, 15, 79, 38, 666 };
    vector<int> vec = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };

    Node* root = creatAVLTree(vec);
    deleteX(root, 2);
    levelTraversal(root);


    system("pause");
    return 0;
}
Node* creatAVLTree(vector<int> vec)
{
    Node* root = NULL;
    for (auto a : vec)
    {
        insert(root, a);
        //updateHeight(root);
        root = reBalance(root);
    }
    return root;
}
void insert(Node* &root, int x)
{
    if (root == NULL)//如果是根节点
    {
        root = new Node;
        root->data = x;
        root->height = 1;
        root->lchild = root->rchild = root->father = NULL;
        return;
    }

    if (root->data < x)
    {
        if (root->rchild == NULL)
        {
            Node* node = new Node;
            node->data = x;
            node->height = 1;
            node->lchild = node->rchild = node->father = NULL;
            root->rchild = node;//建立父子关系
            node->father = root;
        }
        else insert(root->rchild, x);
    }
    else if (x <= root->data)
    {
        if (root->lchild == NULL)
        {
            Node* node = new Node;
            node->data = x;
            node->height = 1;
            node->lchild = node->rchild = node->father = NULL;
            root->lchild = node;//建立父子关系
            node->father = root;
        }
        else insert(root->lchild, x);
    }
}
void deleteX(Node* root, int x)
{
    Node* node = findNode(root, x);//x所在的节点
    if (node == NULL)
    {
        printf("不存在此节点!\n");
        return;
    }
    Node* pre = findPreNode(node);//通过前驱节点来删除；
    Node* suc = findSucNode(node);//通过后继节点来删除；
    //Node* hot = node->father;

    if (node->lchild != NULL && node->rchild != NULL)//左右孩子均存在
    {
        swap(node->data, pre->data);
        node = pre;
    }
    Node* hot = node->father;
    if (node->lchild == NULL && node->rchild == NULL)
    {
        if (hot != NULL)
        {
            hot->lchild == node ? hot->lchild = NULL : hot->rchild = NULL;
        }
        delete node;
    }
    else if (node->lchild == NULL)//左孩子为空
    {
        if (hot != NULL)
        {
            hot->lchild == node ? hot->lchild = node->rchild : hot->rchild = node->rchild;
        }
        node->rchild->father = hot;
        delete node;
    }
    else if (node->rchild == NULL)//右孩子为空
    {
        if (hot != NULL)
        {
            hot->lchild == node ? hot->lchild = node->lchild : hot->rchild = node->lchild;
        }
        node->lchild->father = hot;
        delete node;
    }
    reBalance(root);
    //updateHeight(root);
}
Node* findNode(Node* root, int x)
{
    if (root == NULL || root->data == x) return root;
    if (root->data < x) return findNode(root->rchild, x);
    else return findNode(root->lchild, x);
}
Node* findPreNode(Node* root)
{
    if (root == NULL || root->lchild == NULL) return NULL;
    Node* node = root->lchild;
    while (node->rchild != NULL) node = node->rchild;
    return node;
}
Node* findSucNode(Node* root)
{
    if (root == NULL || root->rchild == NULL) return NULL;
    Node* node = root->rchild;
    while (node->lchild != NULL) node = node->lchild;
    return node;
}

bool isBalance(Node* root)
{
    if (root->lchild == NULL && root->rchild == NULL) return true;
    else if (root->lchild == NULL && root->rchild != NULL)return root->rchild->height <= 1;
    else if (root->lchild != NULL && root->rchild == NULL) return root->lchild->height <= 1;
    else return abs(root->rchild->height - root->lchild->height) <= 1;
}
Node* reBalance(Node* root)
{
    Node *x, *y, *z, *p;//p为第一个非平衡子树根节点的父节点
    x = y = z = NULL;
    x = findBadSubTree(root);
    if (x == NULL)
    {
        cout << "AVL树已经平衡" << endl;
        return root;
    }
    p = x->father;
    y = getSubBadTree(x);
    if (y == NULL) cout << "y出错啦！" << endl;
    z = getSubBadTree(y);
    if (z == NULL) cout << "z出错啦！" << endl;

    Node *a, *b, *c, *T0, *T1, *T2, *T3;
    if (y == x->lchild)
    {
        if (z == y->lchild)
        {
            a = z;
            b = y;
            c = x;
            T0 = z->lchild;
            T1 = z->rchild;
            T2 = y->rchild;
            T3 = a->rchild;
        }
        else
        {
            a = y;
            b = z;
            c = x;
            T0 = y->lchild;
            T1 = z->lchild;
            T2 = z->rchild;
            T3 = x->rchild;
        }
    }
    else
    {
        if (z == y->rchild)
        {
            a = x;
            b = y;
            c = z;
            T0 = x->lchild;
            T1 = y->lchild;
            T2 = z->lchild;
            T3 = z->rchild;
        }
        else
        {
            a = x;
            b = z;
            c = y;
            T0 = x->lchild;
            T1 = z->lchild;
            T2 = z->rchild;
            T3 = y->rchild;
        }
    }
    connect34(a, b, c, T0, T1, T2, T3);
    //if(x->father == NULL)
    if (p == NULL)
    {
        b->father = NULL;
        root = b;
    }
    else if (x == p->lchild)
    {
        p->lchild = b;
        b->father = p;
    }
    else
    {
        p->rchild = b;
        b->father = p;
    }
    updateHeight(root);
    return root;
}
int updateHeight(Node* root)
{
    if (root->lchild == NULL && root->rchild == NULL)
    {
        root->height = 1;
        return root->height = 1;
    }
    else if (root->lchild == NULL && root->rchild != NULL) root->height = updateHeight(root->rchild) + 1;
    else if (root->lchild != NULL && root->rchild == NULL) root->height = updateHeight(root->lchild) + 1;
    else root->height = max(updateHeight(root->lchild), updateHeight(root->rchild)) + 1;
}
Node* findBadSubTree(Node* root)
{
    updateHeight(root);
    if (root == NULL) return NULL;
    stack<Node*> sta;
    while (true)
    {
        if (isBalance(root) == false)
        {
            return root;
        }
        if (root->rchild != NULL) sta.push(root->rchild);
        if (root->lchild != NULL) sta.push(root->lchild);
        if (sta.empty()) break;
        root = sta.top();
        sta.pop();
    }
    return NULL;
}
Node* getSubBadTree(Node* root)
{
    if (root->lchild != NULL && root->rchild != NULL)
    {
        return root->lchild->height > root->rchild->height ? root->lchild : root->rchild;
    }
    else if (root->lchild != NULL && root->rchild == NULL) return root->lchild;
    else if (root->lchild == NULL && root->rchild != NULL) return root->rchild;
    return NULL;
}
void connect34(Node* a, Node* b, Node* c, Node* T0, Node* T1, Node* T2, Node* T3)
{
    b->lchild = a, a->father = b;
    b->rchild = c, c->father = b;
    a->lchild = T0; if (T0 != NULL) T0->father = a;
    a->rchild = T1; if (T1 != NULL) T1->father = a;
    c->lchild = T2; if (T2 != NULL) T2->father = c;
    c->rchild = T3; if (T3 != NULL) T3->father = c;
}

//输出
void levelTraversal(Node* root)
{
    queue<Node*> Q;
    Q.push(root);
    root->level = 1;
    int nowLevel = root->level;
    printf("第%d层：\n", nowLevel);
    while (!Q.empty())
    {
        Node* front = Q.front();
        Q.pop();
        int level = front->level;
        if (level != nowLevel)
        {
            nowLevel = level;
            printf("\n第%d层：\n", nowLevel);
        }
        printf("%d height = %d\n", front->data, front->height);
        if (front->lchild != NULL)
        {
            Q.push(front->lchild);
            front->lchild->level = level + 1;
        }
        if (front->rchild != NULL)
        {
            Q.push(front->rchild);
            front->rchild->level = level + 1;
        }
    }
    printf("\n");
}